Find the kinetic energy required to project an object of mass $m$ from the surface of the Earth to infinity.

The angular velocity of rotation of a star (of mass $M$ and radius $R$) at which the matter starts to escape from its equator will be:

The escape velocity for the earth is $11.2 \ km/s$. The mass of another planet is $100$ times that of the earth and its radius is $4$ times that of the earth. The escape velocity for this planet will be ......... $km/s$.

$A$ body is projected vertically upwards from the Earth's surface with a velocity $2 v_{e}$,where $v_{e}$ is the escape velocity from the Earth's surface. The velocity of the body when it escapes the gravitational pull is

$v_e$ and $v_p$ denote the escape velocity from the Earth and another planet having twice the radius and the same mean density as the Earth. Then:

If the escape velocity on Earth is $11.2 \text{ km/s}$, what is its value for a planet having double the radius and $8$ times the mass of Earth (in $\text{ km/s}$)?